Euler's theorem as the path towards geometry

Abstract

The course in Mathematics for Architecture Students at the Technion-Israel Institute of Technology needed to encapsulate as much formative knowledge as possible. Above and beyond the absolute importance of Euler's Formula relative to the corpus of classical mathematics and the role it played in its development (as in Betti numbers and Homology in general on one hand and the Global Gauss-Bonnet Theorem on the other hand), its simplicity, yet potency (in the sense of representing a spring board, an opening towards a variety of subjects belonging to the fields of Topology and Geometry) recommend Euler's Theorem as natural candidate for a cornerstone, a red thread running through and directing the whole course. © Birkhäuser Verlag, Basel 2005.